Sub-ballistic operator growth in spin chains with heavy-tailed random fields
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913962996531200 |
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| author | Baldwin, Christopher L. |
| author_facet | Baldwin, Christopher L. |
| contents | We rigorously prove that in nearly arbitrary quantum spin chains with power-law-distributed random fields, namely such that the probability of a field exceeding $h$ scales as $h^{-α}$, it is impossible for any operator evolving in the Heisenberg picture to spread with dynamical exponent less than $1/α$. In particular, ballistic growth is impossible for $α< 1$, diffusive growth is impossible for $α< 1/2$, and any finite dynamical exponent becomes impossible for sufficiently small $α$. This result thus establishes a wide family of models in which the disorder provably prevents conventional transport. We express the result as a tightening of Lieb-Robinson bounds due to random fields -- the proof modifies the standard derivation such that strong fields appear as effective weak interactions, and then makes use of analogous recent results for random-bond spin chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-ballistic operator growth in spin chains with heavy-tailed random fields Baldwin, Christopher L. Disordered Systems and Neural Networks Mathematical Physics Quantum Physics We rigorously prove that in nearly arbitrary quantum spin chains with power-law-distributed random fields, namely such that the probability of a field exceeding $h$ scales as $h^{-α}$, it is impossible for any operator evolving in the Heisenberg picture to spread with dynamical exponent less than $1/α$. In particular, ballistic growth is impossible for $α< 1$, diffusive growth is impossible for $α< 1/2$, and any finite dynamical exponent becomes impossible for sufficiently small $α$. This result thus establishes a wide family of models in which the disorder provably prevents conventional transport. We express the result as a tightening of Lieb-Robinson bounds due to random fields -- the proof modifies the standard derivation such that strong fields appear as effective weak interactions, and then makes use of analogous recent results for random-bond spin chains. |
| title | Sub-ballistic operator growth in spin chains with heavy-tailed random fields |
| topic | Disordered Systems and Neural Networks Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2409.17242 |